[mikhailfranco]

One of the few comments here that shows great insight. I think you should push the argument down a few layers, to talk about the discreteness of quantum observables, the underlying unobservable continuous wavefunction, and the randomness of the Born rule that maps between the two (Copenhagen collapse or forking of Many Worlds).

Tegmark takes a similar, but rather extreme, MW approach in his book 'Our Mathematical Universe'.

Personally, I struggle with Tegmark's use of Measure Theory, and proponents of various Anthropic Principles, because they seem to have a completely broken frequentist view of probability and inference.